I'm trying to create a football game where the user will make a flick gesture in order to kick the ball. I'm quite new to developing games in unity3d, I have successfully made a moving ball, added some rotation, gravity and some basic input (the ball follows the touch coordinates). How can I achieve the flick gesture?

Use the position returned from drag begin and drag end to determine the magnitude and direction of the drag, and record the start and end times in the event handlers to see how fast the gesture was. A drag done quickly is a flick.

If you want to stay in the "Unity state of mind" and keep your code platform independent (even if just so you can easily test on your desktop), I found the easiest way to handle gestures is using one of the gesture plugins.